Some of these works have been lent to serious and scholarly museum shows in the United States, Japan, and Europe. Agreeing to such loans is common practice, and builds goodwill for when the museum asks to borrow for its own exhibitions.

However, the MFA, eager to raise revenues, is also renting out many of its most prized works of European and American art to for-profit enterprises. A total of 26 paintings, including the marquee “Dance at Bougival” and “Madame Roulin,” have been sent to exhibitions in Italy organized by a private company called Linea d’Ombra, for a large, undisclosed fee.

The combined loans and rentals have resulted in what Malcolm Rogers, the MFA’s director, readily admits is a “traffic jam” of missing masterpieces.

“We admit there is some crowding [on the list of masterpieces sent away],” Rogers said in an interview with the Globe. “Everything has come together at once.”

The practice of charging fees for lending works is not new, but it remains controversial. The Italian shows currently showing works from the MFA, in the cities of Vicenza and Verona, are titled “Raphael to Picasso” and “From Botticelli to Matisse.”

Linea d’Ombra is run by art historian-turned-entrepreneur Marco Goldin, an impresario who has been dubbed the “King Midas of the art world” by newspapers in Italy. During the past decade, Goldin has found success persuading northern Italian cities to pay steep fees to mount popular exhibitions of borrowed artworks.

‘As an art history professor, it seems perfectly reasonable to expect that certain canonical masterpieces are on display in the museum,’ said Jonathan Unglaub of Brandeis University.

Goldin promises that these exhibitions will boost local economies and do wonders for the host city’s image. “Raphael to Picasso” attracted 100,000 in its first 47 days.

Renowned as a showman, Goldin uses aggressive marketing to promote the exhibits, beginning up to a year in advance with package tours, glossy catalogs published in house by Linea d’Ombra, mass mailings, pamphlets inserted in local newspapers, TV ads, and even a “Monet card” offering discounts at local restaurants and stores, and for transportation and other services.

Nonetheless, Goldin believes fervently in the high quality of his exhibitions. “I like so much to tell stories about art with very high quality paintings,” he said in an e-mail to the Globe.

The MFA is the biggest lender to the exhibitions in Vicenza and Verona, but it is not the only major institution involved. Other lenders include the National Galleries of Scotland in Edinburgh and the Wadsworth Athenaeum in Hartford. Museums that have lent generously to previous Linea d’Ombra’s exhibitions include the Louvre and the Musee d’Orsay in Paris, and the Van Gogh Museum in Amsterdam.

In 2008, partly in response to Linea d’Ombra’s success, the Italian branch of the International Council of Museums put out a paper condemning the practice of charging for loans. It noted its own ethical code, which states that museum collections are for the benefit of the public and should never be considered financial assets.

According to Anna Somers Cocks, founder, editor, and chief executive of The Art Newspaper, “Italy’s towns are wasting millions on importing these potboiler exhibitions instead of putting the money . . . into bringing their own museums and cultural monuments into the 21st century, so that they would have something lasting and growing.

“This has come about,” she told the Globe, “because the [Italian] museums are run according to such rigid and antiquated rules that they cannot rival Goldin’s marketing skills. The towns know they can’t make the money back just in ticket sales, but believe that there is a wider economic benefit.”

Educators in the Boston area’s art schools, high schools, and colleges are particularly frustrated.

“As an art history professor, it seems perfectly reasonable to expect that certain canonical masterpieces are on display in the museum,” said Brandeis University’s Jonathan Unglaub, chairman and associate professor of fine arts. “Having major works off-view compromises, even undermines, my teaching. For the Art History Survey, for instance, it is . . . essential to teach in front of . . . the best Manet painting available, namely, ‘The Street Singer.’ Sadly, this major masterpiece seems often to be MIA.”

Unglaub believes the museum has “a sacred duty to display its permanent collection to the greatest extent possible to its core regional audience, and as a mecca for tourists and visitors.”

According to Rogers, “Some of the people who say, ‘Why is such and such away?’ are often the same people who say, ‘But why aren’t you putting on display more things from storage?’ So we’re increasingly rotating.

“Now, perhaps the balance is wrong this year. But we really do try to balance it. We say no to major prestigious loans frequently.”

Asked if he was concerned about art lovers and teachers coming to the MFA and finding key works missing, Rogers replied: “We all have that experience of going to a museum and wanting to find something and finding the gallery is closed. . . . Sadly, people will always want the very best things on display.”

However, he also feels that “we should be represented abroad by the very best things in our collection. We do try to be discerning. But we also want to keep our exhibition program going and we need the income coming in.”

In just seven years, the MFA has lent works to 14 exhibitions organized by Linea d’Ombra (it has declined to lend to six more). The first, in October 2005, was an exhibition of 60 works by Millet from the MFA’s own collection, which traveled to Brescia, with a catalog coauthored by Goldin and George Shackelford, the former MFA chairman of the art of Europe.

That show, Rogers notes, was the first major exhibition by Millet to be shown in Italy, and a “high point” in the MFA’s collaboration with the Italian company. At the same time, the MFA lent four paintings and eleven works on paper to a second Linea d’Ombra show, “Gauguin Van Gogh.”

“I felt we were contributing to the cultural history of Italy,” says Rogers, who, in 2009, was made Commander of the Order to the Merit of the Italian Republic, one of the highest honors presented by the president of the Italian Republic, for fostering cultural cooperation between the MFA and Italy.

Other Linea d’Ombra shows the MFA has lent generously to include “Masterpieces of European Art” in Rimini in 2009-2010, and the previous year, “America!” which Goldin described as “the largest exhibition, in Europe, dedicated to American art and culture of the 19th century.”

Since he arrived at the MFA in 1994, Rogers says he has focused on “building the MFA’s reputation in other countries, and on sharing its treasures with audiences who may not come here.”

The current rentals to Linea d’Ombra’s Italian shows, which also include two paintings by John Singleton Copley, two paintings by Manet, two Rembrandt portraits, a Delacroix, a Veronese, a Gentile Bellini, a second Renoir, a Winslow Homer, a Gainsborough, a Sargent, a Cranach, a Gauguin, a Giacometti and a Picasso, are part of this strategy, he says.

Most of the works the MFA sends to temporary exhibitions in other museums do not raise revenue. If a fee is charged, it’s usually a modest processing fee to cover administration costs.

“We’d rather not do it,” says Katie Getchell, the MFA’s deputy director. According to Rogers, the MFA charges fees only “when there’s an established tradition of doing so.”

But Rogers acknowledges that it has also been part of the MFA’s strategy to develop “a program of creating major touring exhibitions that bring revenue to the museum. “Many of them,” he says, “use as their springboard the museum in Nagoya [Nagoya/Boston Museum of Fine Arts, with which the MFA has had a partnership for 13 years],” meaning that shows created for Nagoya then move to other host museums around the world. “We charge a fee because they are created specifically to tour as a service to other people. The fees are hugely beneficial [to the MFA].”

The incoming funds can be used wherever needed, such as to help cover conservation costs and pay salaries, explains Rogers. He says the MFA’s financial situation is unusually tight.

“The value of the endowment is down. Attendance is good but it is nevertheless a little soft because of economic uncertainty. The climate affects membership, it affects all sorts of things. We are a very lean organization and it’s extraordinary what we achieve. But we have to raise resources in a variety of ways and we have to be prudent about staffing levels, and I want to preserve jobs that we have. Every year is a knife edge.”

The touring shows, claims Rogers, are a form of educational outreach and they help to market the museum abroad.

However, in a 2008 column in The Art Newspaper, Somers Cocks warned that great lending museums like the MFA “risk killing the goose that lays the golden eggs. After all, why should they be deserving of tax-free status, of donations from business and the rich, of being considered superior to ordinary commercial life if they themselves become so commercial as to rent our their collections?”

In his interview with the Globe, Rogers acknowledged for the first time that he intends to continue indefinitely as chairman of the art of Europe, supervising all aspects of the MFA’s vast European art holdings. He took up the position, for which he draws no extra salary, last year — saying it would only be temporary — after Shackelford left to be the deputy director of the Kimbell Art Museum in Fort Worth.

But some observers worry that, by appointing himself as chairman of the art of Europe, Rogers has no senior curator challenging his decisions that are focused more on fund-raising than on what is best for the collection, and best for the museum’s local audience — including visitors to Boston.

Sebastian Smee is the Globe’s art critic. He can be reached at ssmee@globe.com.

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